158 lines
7.9 KiB
Python
Executable File
158 lines
7.9 KiB
Python
Executable File
#!/usr/bin/env python3
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import math
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from qpms.argproc import ArgParser, sfloat
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ap = ArgParser(['const_real_background', 'lattice2d', 'multi_particle']) # TODO general analytical background
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ap.add_argument("-k", nargs=2, type=sfloat, required=True, help='k vector', metavar=('K_X', 'K_Y'))
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ap.add_argument("--kpi", action='store_true', help="Indicates that the k vector is given in natural units instead of SI, i.e. the arguments given by -k shall be automatically multiplied by pi / period (given by -p argument)")
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ap.add_argument("--rank-tol", type=float, required=False)
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ap.add_argument("-o", "--output", type=str, required=False, help='output path (if not provided, will be generated automatically)')
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ap.add_argument("-t", "--rank-tolerance", type=float, default=1e11)
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ap.add_argument("-c", "--min-candidates", type=int, default=1, help='always try at least this many eigenvalue candidates, even if their SVs in the rank tests are lower than rank_tolerance')
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ap.add_argument("-T", "--residual-tolerance", type=float, default=2.)
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ap.add_argument("-N", type=int, default="150", help="Integration contour discretisation size")
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#TODO alternative specification of the contour by center and half-axes
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dospec = ap.add_argument_group("Eigenvalue search area by diffracted order specification", "Specification of eigenvalue search area by diffracted order number (requires constant real refractive index for background): the integration contour 'touches' the empty lattice band specified by -b, and its axis lying on the real axis reaches '-f'-way to the next diffractive order")
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dospec.add_argument("-d", "--band-index", type=int, help="Argument's absolute value determines the empty lattice band order (counted from 1), -/+ determines whether the eigenvalues are searched below/above that empty lattice band.", required=True)
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dospec.add_argument("-f", "--interval-factor", type=float, default=0.1, help="Relative length of the integration ellipse axis w.r.t. the interval between two empty lattice bands; this should be be less than 1.") #TODO check
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dospec.add_argument("-i", "--imaginary-aspect-ratio", type=float, default=1., help="Aspect ratio of the integration ellipse (Im/Re); this should not exceed 1/interval_factor.")
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ap.add_argument("-P", "--plot", action='store_true', help="if -p not given, plot to a default path")
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ap.add_argument("-O", "--plot-out", type=str, required=False, help="path to plot output (optional)")
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a = ap.parse_args()
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a1 = ap.direct_basis[0]
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a2 = ap.direct_basis[1]
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particlestr = "modes" # TODO particle string specifier or some hash, do this in argproc.py
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defaultprefix = "%s_basis%gnm_%gnm__%gnm_%gnm_n%g_b%+d_k(%g_%g)um-1_cn%d" % (
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particlestr, a1[0]*1e9, a1[1]*1e9, a2[0]*1e9, a2[1]*1e9, a.refractive_index, a.band_index, a.k[0]*1e-6, a.k[1]*1e-6, a.N)
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import logging
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logging.basicConfig(format='%(asctime)s %(message)s', level=logging.INFO)
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import numpy as np
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import qpms
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from qpms.cybspec import BaseSpec
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from qpms.cytmatrices import CTMatrix
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from qpms.qpms_c import Particle, ScatteringSystem, empty_lattice_modes_xy
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from qpms.cymaterials import EpsMu, EpsMuGenerator, LorentzDrudeModel, lorentz_drude
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from qpms.constants import eV, hbar
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eh = eV/hbar
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def inside_ellipse(point_xy, centre_xy, halfaxes_xy):
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x = point_xy[0] - centre_xy[0]
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y = point_xy[1] - centre_xy[1]
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ax = halfaxes_xy[0]
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ay = halfaxes_xy[1]
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return ((x/ax)**2 + (y/ay)**2) <= 1
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beta = np.array(a.k)
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if True: # TODO alternative specification of the contour by center and half-axes
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empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, np.array([0,0]), 1)
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empty_freqs = empty_lattice_modes_xy(ap.background_epsmu, ap.reciprocal_basis2pi, beta, (1+abs(a.band_index)) * empty_freqs[1])
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# make the frequencies in the list unique
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empty_freqs = list(empty_freqs)
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i = 0
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while i < len(empty_freqs) - 1:
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if math.isclose(empty_freqs[i], empty_freqs[i+1], rel_tol=1e-13):
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del empty_freqs[i+1]
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else:
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i += 1
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logging.info("Empty freqs: %s", str(empty_freqs))
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logging.info("Empty freqs (eV): %s", str([ff / eh for ff in empty_freqs]))
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if a.band_index > 0:
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top = empty_freqs[a.band_index]
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bottom = empty_freqs[a.band_index - 1]
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lebeta_om = bottom
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else: # a.band_index < 0
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top = empty_freqs[abs(a.band_index) - 1]
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bottom = empty_freqs[abs(a.band_index) - 2] if abs(a.band_index) > 1 else 0.
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lebeta_om = top
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#print(top,bottom,lebeta_om)
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freqradius = .5 * (top - bottom) * a.interval_factor
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centfreq = bottom + freqradius if a.band_index > 0 else top - freqradius
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if freqradius == 0:
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raise ValueError("Integration contour radius is set to zero. Are you trying to look below the lowest empty lattice band at the gamma point?")
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freqradius *= (1-1e-13) # to not totally touch the singularities
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logging.info("Direct lattice basis: %s" % str(ap.direct_basis))
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logging.info("Reciprocal lattice basis: %s" % str(ap.reciprocal_basis2pi))
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ss, ssw = ScatteringSystem.create(ap.get_particles(), ap.background_emg, centfreq, latticebasis=ap.direct_basis)
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logging.info("Finding eigenvalues around %s (= %s eV)" % (str(centfreq), str(centfreq/eh)))
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logging.info("Real half-axis %s (= %s eV)" % (str(freqradius), str(freqradius/eh)))
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logging.info("Imaginary half-axis %s (= %s eV)" % (str(freqradius*a.imaginary_aspect_ratio), str(freqradius*a.imaginary_aspect_ratio/eh)))
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with qpms.pgsl_ignore_error(15):
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res = ss.find_modes(centfreq, freqradius, freqradius * a.imaginary_aspect_ratio,
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blochvector = a.k, contour_points = a.N, rank_tol = a.rank_tolerance,
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res_tol = a.residual_tolerance, rank_min_sel = a.min_candidates)
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logging.info("Eigenfrequencies found: %s" % str(res['eigval']))
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logging.info("Eigenfrequencies found (eV): %s" % str(res['eigval'] / eh))
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res['inside_contour'] = inside_ellipse((res['eigval'].real, res['eigval'].imag),
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(centfreq.real, centfreq.imag), (freqradius, freqradius * a.imaginary_aspect_ratio))
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#res['refractive_index_internal'] = [emg(om).n for om in res['eigval']]
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#del res['omega'] If contour points are not needed...
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#del res['ImTW'] # not if dbg=false anyway
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outfile = defaultprefix + ".npz" if a.output is None else a.output
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np.savez(outfile, meta=vars(a), empty_freqs=np.array(empty_freqs), **res)
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logging.info("Saved to %s" % outfile)
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if a.plot or (a.plot_out is not None):
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if len(res['eigval']) == 0:
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logging.info("No eigenvalues found; nothing to plot")
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exit(1)
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imcut = np.linspace(0, -freqradius)
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recut1 = np.sqrt(lebeta_om**2+imcut**2) # incomplete Gamma-related cut
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recut2 = np.sqrt((lebeta_om/2)**2-imcut**2) + lebeta_om/2 # odd-power-lilgamma-related cut
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import matplotlib
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matplotlib.use('pdf')
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from matplotlib import pyplot as plt
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fig = plt.figure()
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ax = fig.add_subplot(111,)
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#ax.plot(res['omega'].real/eh, res['omega'].imag/eh*1e3, ':') #res['omega'] not implemented in ScatteringSystem
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ax.add_artist(matplotlib.patches.Ellipse((centfreq.real/eh, centfreq.imag/eh*1e3),
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2*freqradius/eh, 2*freqradius*a.imaginary_aspect_ratio/eh*1e3, fill=False,
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ls=':'))
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ax.scatter(x=res['eigval'].real/eh, y=res['eigval'].imag/eh*1e3 , c = res['inside_contour']
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)
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ax.plot(recut1/eh, imcut/eh*1e3)
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ax.plot(recut2/eh, imcut/eh*1e3)
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for i,om in enumerate(res['eigval']):
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ax.annotate(str(i), (om.real/eh, om.imag/eh*1e3))
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xmin = np.amin(res['eigval'].real)/eh
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xmax = np.amax(res['eigval'].real)/eh
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xspan = xmax-xmin
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ymin = np.amin(res['eigval'].imag)/eh*1e3
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ymax = np.amax(res['eigval'].imag)/eh*1e3
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yspan = ymax-ymin
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ax.set_xlim([xmin-.1*xspan, xmax+.1*xspan])
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ax.set_ylim([ymin-.1*yspan, ymax+.1*yspan])
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ax.set_xlabel('$\hbar \Re \omega / \mathrm{eV}$')
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ax.set_ylabel('$\hbar \Im \omega / \mathrm{meV}$')
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plotfile = defaultprefix + ".pdf" if a.plot_out is None else a.plot_out
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fig.savefig(plotfile)
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exit(0)
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